A Lower Bound on the Average Degree Forcing a Minor

Sergey Norin, Bruce A Reed, Andrew G Thomason, David R Wood

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We show that for sufficiently large d and for t≥d+1, there is a graph G with average degree (1−ε)λt√lnd such that almost every graph H with t vertices and average degree d is not a minor of G, where λ=0.63817… is an explicitly defined constant. This generalises analogous results for complete graphs by Thomason (2001) and for general dense graphs by Myers and Thomason (2005). It also shows that an upper bound for sparse graphs by Reed and Wood (2016) is best possible up to a constant factor.
Original languageEnglish
Article numberP2.4
Number of pages9
JournalThe Electronic Journal of Combinatorics
Issue number2
Publication statusPublished - 2020

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